Effective low energy theory for surface Andreev bound states of superconducting phases in generalized Bernevig-Hughes-Zhang models

摘要

A method for constructing the low energy effective models for pairings in thegeneralized Bernevig-Hughes-Zhang model for materials like Bi$_{2}$Se$_{3}$ isproposed. Pairings in this two-orbital model are identified with those familiarin one-orbital models, enabling a unified understanding. The theory provides aneasy way to understand the topological nature of the superconducting state thatis not directly related to the topological order in the normal state but due tosubtle coupling among the degrees of freedom. Furthermore this approach shows asimple way to characterize the anisotropic nature of surface Andreev boundstates (SABSs). In particular, we have identified the conditions to have asurprising new result of having two pairs of SABSs. It also leads to aconclusion that SABSs always connect with the topological surface states if thelatter are well defined at the chemical potential.